The stability we need to explore is related to the presence of
massive spin-2 ghost degrees of freedom, which means the transverse
and traceless modes of the metric perturbation on the homogeneous
and isotropic, cosmological background.
According to the theory of cosmological perturbations
(see, e.g., [1]}, [2]}, [3]}), the
background cosmological metric with tensor perturbations is
\(\mathrm {d}s^2\,=\,a^2(\eta ) \big [ \mathrm {d}\eta ^2 - \left(\gamma _{ij} + h_{ij}\right)\mathrm {d}x^i\mathrm {d}x^j \big ],\) 
